Transcript STAT111 Introductory Statistics

The UNIVERSITY of NORTH CAROLINA
at CHAPEL HILL
STOR 155 Introductory Statistics
Lecture 1: Overview
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Registration Issues
• Contact Charlotte Rogers:
Hanes 321, 962-2307,
[email protected]
• Fill out some paperwork with her to be put
on the waiting list.
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My Strategy for Success
• Stay active/involved in class.
• Ask questions during class (especially if you do not
understand something).
– Do not feel shy or stupid.
• Answer questions to help other students if you
can.
• Keep pace with the lectures, review daily, do
homework after each lecture to help understand
the materials.
• Make effective use of office hours (Instructor and
IA) and open tutorial sessions
– Help you to answer questions about homework and
lectures
– Private time vs. public time
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What is Statistics?
• "Data! Data! Data!" he cried impatiently. "I
can't make bricks without clay."
----Sherlock Holmes
The Adventures of the Copper Beeches
• "Data! Data! Data!" he yelled loudly. "I
can't teach Statistics without Data."
----Instructor
Introductory Statistics
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What is Statistics?
• Statistics: the science of collecting,
organizing, and interpreting data.
Population
Inference about population
(using statistical tools)
Sample of
data
• data = information
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How can Statistics help us?
•
claims that it contains 1000 chips. Is
this true?
• Among a group of randomly chosen people, how
likely is it for two of them to have the same
birthday?
• What is the relationship between Income and
Years of Education?
• Design your own experiment, collect data,
analyze data and draw conclusions.
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SAT Scores
• Parents and teachers have been concerned about the trend of
declining SAT scores and sought ways to halt the decline.
• One question: the effect of classroom atmosphere (strict or
liberal).
• To answer the question, 50 students (24 males and 26
females) participated in a study on student performance, as
measured by SAT scores at the end of the school year.
• The students were divided into two groups of 25 each (12
males and 13 females), with Group 1 to study under a strict
atmosphere while Group 2 under a very permissive
atmosphere.
• They were matched according to socio-economic background.
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SAT Scores
• After nine months, all students were given
the same standardized tests: the verbal test
and the mathematics test.
Student
A
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Group Gender
Strict
F
SATMath
670
SATVer
700
B
C
D
Strict
Liberal
Liberal
M
F
M
700
750
690
680
730
750
…
…
…
…
…
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SAT Scores
• This example involves data collection, data
analysis, and statistical inference.
– How?
• Questions:
– Does stricter classroom atmosphere increase the
average score?
– Why “matched according to socio-economic
background”?
– Why “12 males and 13 females per group”?
– Is the group size 50 large enough to make a confident
conclusion?
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Fundamental Concepts
• Population: the entire group of individuals that we
want information about.
– Students (who are about to take SAT)
• Sample: a part of the population that we actually
examine in order to gather information.
– those students selected into the study
• Sample size: number of observations/individuals in a
sample.
– 50
• Statistical inference: to make an inference about a
population based on the information contained in a
sample.
– Based on the data from the study, to infer whether a stricter
classroom atmosphere increases SAT scores in general.
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Fundamental Concepts
• A parameter is a value that describes the
population. It’s fixed but unknown in practice.
– the average SAT score of all the students, who are
about to take SAT.
• A statistic is a value that describes a sample. It’s
known once a sample is obtained.
– the average SAT score of all the students, who are
selected into the study.
– a sample analogy of the parameter.
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Practice Exercise
• Suppose you are interested in finding out
the average SAT score of UNC unders,
– The SAT scores of all UNC unders in
STOR155
– The SAT scores of all UNC unders
• Suppose you are interested in finding out
the average SAT score of US unders,
– The SAT scores of all UNC unders
– The SAT scores of all US unders
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Take Home Message
• Statistics is the science of data:
– Collecting
– Analyzing
– Decision making
= Information processing
• Fundamental concepts:
– Population, parameter, sample, statistic, sample
size
• You can do a LOT with statistics … what ?
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Take home message
• Interested in population, but it’s too large
to become known completely
• Statisticians work on sample, which is a
smaller and observable ``proxy’’
• There is uncertainty in this transition,
hence errors are inevitable …
• That’s why statistical methods are needed
…
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